Showing Page:
1/3
В-4
1.
Cxxxdx
x
xxdx
x
xx
++=
+=
+
ln2
4
3
3
22
3
23
4
2
3
3
2
1
43
2.
=
+
+
+
=
+
+
+
=
+
+
13
6
6
1
3
1
3
5
1313
5
13
5
2
2
222
x
xdx
x
dx
x
xdx
x
dx
dx
x
x
( )
( )
( )
Cxxarctg
x
xd
x
dx
+++=
+
+
+
+
=
13ln
6
1
3
3
5
13
13
6
1
3
1
3
5
2
2
2
2
3.
( )
2
2 2 2 2
2
32
5 1 4 1 5
5
3
4 4 2
3 2 3 2 3 2 3 2
2
dx
x xdx dx dx
dx
x x x x
x
−−
= = + =
22
3
1 5 2 1 5 2 3
2
3 2 3 2
4 2 4
2 3 3 2 6 2 3
2
x
x
ln x ln C ln x ln C
x
x
= + + = + +
+
+
4.6.
( ) ( )
=
+
=
+
++
=
+
dx
x
xdx
x
xxx
dx
x
x
1
1
22
1
1122
1
32
2
2
2
224
2
4
Carctgxxx += 2
3
2
3
5.
Cxx += 4sin
12
1
4sin
4
1
3
6.
Cxxxdxdxx +==
2cos
10
1
)2(cos2cos
2
1
2sin2cos
544
7.
( ) ( )
=
+
+
+
+
=
+
12164
4
12164
168
8
1
12164
2
222
xx
dx
xx
dxx
xx
dxx
( )
( )
C
x
x
xx
x
dx
xx
xxd
+
++
+
++=
+
+
+
+
=
72
72
ln
72
1
12164ln
8
1
72
12164
12164
8
1
2
22
2
8.
( ) ( )
( )
2
2 2 2 2 2
3 3 16
2 13 6 3
1 1 12
12
33
3
3 3 16 3 3 16 3 3 16 3 3 16
1 67
2 12
d x x
x dx x dx
dx dx
x x x x x x x x
x
−−
−−
= = =

−+


22
1 1 16
3 3 16 4 3
2 2 3
x x ln x x x C= + + +
9.
( )
=+==
=
=
=+
=
=
+
C
t
t
tdt
t
dt
ttg
tdt
t
dt
dx
t
x
tgtx
xx
dx
sin9
1
sin
cos
9
1
cos
cos
9
1
cos
3
cos
9
9
3
9
222
2
2
2
22
1
2
2
2
22
9
9
9
sin
9
9
sin1cos
C
x
x
x
x
t
x
tt
+
+
=
+
=
+
==
=
Showing Page:
2/3
10.
( )
( )
2
32
2
1
1
32
dx
u ln x;du
x
x x ln xdx
xx
dv x x dx;v x
==
+ = =
= + = +
Cx
xx
xx
xx
dx
xx
xx
xx
++
+=
+
+=
49
ln
23
1
23
ln
23
2323223
11. Ответ не совпадает
( )( )
=
=
=
+
=
===
xv
x
dx
dv
xx
dx
x
dx
duxu
частямпо
dx
x
x
12
1
11
1
arcsin
_
1
arcsin
2
Cxxx
x
dx
xx +++=
+
+=
14arcsin12
1
2arcsin12
12.
( )
===
xdxx
x
dxxxxdxx 2cos
2
1
4
2cos1
2
1
sin
2
2
Cxx
xx
xdxxx
x
xvxdxdv
dxduxu
частямпо
+=
==
==
===
2cos
8
1
2sin
44
2sin2sin
4
1
4
2sin
2
1
2cos
_
2
2
13.
( )
( )
( )( )( )
=
++
=
++
dx
xxx
x
dx
xxx
x
211
6
123
6
2
2
2
( )( )( )
( )( ) ( )( ) ( )( )
( )( )( )
Cxxx
x
dx
x
dx
x
dx
C
B
A
Cxпри
Bxпри
Axпри
xxx
xxCxxBxxA
x
C
x
B
x
A
xxx
x
++++=
+
+
+
=
=
=
=
=
==
==
==
++
++++++
=
=
+
+
+
+
=
++
=
2ln81ln31ln
2
8
1
3
1
8
3
1
2432_
621_
661_
211
112112
211211
6
2
14.
( )
( )
( )
( )( )
( )
=
=
=
=
=++=
==
==
+
+++
=++
+
=
+
+
=
+
+
=
+
+
2
1
1
3221_
11_
20_
1
1
1
1
2
1
)2(2
2
2
22
223
C
B
A
CBAxпри
Axпри
Cxпри
xx
xCBxAx
x
С
x
B
x
A
xx
x
xx
dxx
dx
xx
x
Cxx
xx
dx
x
dx
x
dx
+++=
+
+=
1lnln
2
1
2
2
15.
( )
( )
=
++
+
dx
xxx
x
1022
222
2
Showing Page:
3/3
( )
( )
( )
( )( )
( )
( )
=
=
=
=
=+
=+
=
=
++
++++
=
+
+
+
+
=
++
+
=
6
1
1
22210
0
1818
2
1022
2102
102
2
1022
222
0
2
2
2
22
C
B
A
CA
BA
A
x
x
x
xxx
xCBxxxA
xx
СBx
x
A
xxx
x
( )
( )
C
x
arctgxxx
x
dx
xx
xxd
x
dx
xx
dx
xx
dxx
x
dx
xx
dxx
x
dx
+
+++=
+
+
+
+
+
=
=
+
+
+
+
=
+
+
+
=
3
1
3
5
102ln
2
1
2ln
91
5
102
102
2
1
2
102
5
102
)22(
2
1
2
102
)6(
2
2
22
2
222
16.
( )
( )
=
=
=
=
=
+=
=
++
3
2
3
2
2
4
4
41
22
2
t
dt
tt
tdt
tdtdx
tx
xt
xx
dx
1
34
34
ln
3
1
3
3
ln
3
1
C
x
x
C
t
t
+
++
+
=+
+
=
17.
=
+
=
+
=
=
=
=+
=+
+=
=
+++
+
dt
t
t
dtt
tt
t
dttdx
tx
tx
tx
xt
dx
xx
x
1
66
6
3
3
3
3
33
3
7
5
2
3
5
6
3
2
3
6
63
( ) ( ) ( ) ( )
( ) ( ) ( )
1
663
6
4
6
5
6
7
234567
23456
13ln63633
323
2
3
3
5
6
)3(3
7
6
1ln6632
2
3
5
6
7
6
1
1
16
Cxxx
xxxxx
Ctttttttt
dt
t
tttttt
++++++
+++++++=
=+++++=
=
+
+++=
18.
( )
=
+
=
=
+
=
+
=
+
=
=
=
232146
2
1
1
cos
1
2
sin
1
2
2
cos4sin3
22
2
2
2
2
tt
dt
tt
dt
t
t
x
t
t
x
t
dt
dx
x
tgt
xx
dx
( )
( )
1
2
22
2
1
2
ln
5
1
4
5
4
3
4
5
4
3
ln
5
1
16
25
4
3
2
1
C
xtg
xtg
C
t
t
t
dt
+
+
=+
++
+
=
+
=
19. Ответ не совпадает
2
2
22
2
2 2 2 2
2
1
1
4
3 4 1 4 1
1
t
t tgx;sin x
sin x sin x dx
t
dx dx dx
dt
sin x cos x sin x sin x
dx
t
==

+
= = + = =


=
+
( ) ( )
12
2
11
33
4 4 4
31
33
dt x x x
C arctg t C arctg tgx C
t
= + + = + + = + +
20.
( )
=+=+=
xdxxxdxdxxxxdxx 4cos4sin
8
1
4sin
8
1
4cos14sin
8
1
2cos2sin
22242
( ) ( )
Cxxxxxddxx ++=+=
4sin
96
1
8sin
128
1
16
1
4sin4sin
32
1
8cos1
16
1
32

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